no, balanced operation is about common noise rejection and isolation from ground, therefore less crosstalk between left and right channels, the fact that the level is higher is a byproduct of the single ended implementation inside the dac being 'doubled' to achieve balanced effect (basically having two inverted single ended sources/output to achieve one balanced, minus ground wire in the signal path), so out of practicality and common sense not to mess with the signal level more than it's necessary it's left to be twice that of the single ended output, also it's an industry standard for pro gear
pre-gain is used for overall level matching before gain because of the huge difference in sensitivity and impedance between various headphones/iems, basically a fixed resistor (stepped attenuator is you wish) pot before gain stage so to have more (or less, in that case it increases gain by looping) headroom with the main knob pot
but one must be aware that pre-gain value will sum up to the source level, so if like with the v200 the max input level is 21dBu for balanced input and your dac (source) output level is 15dBu (v800 default level for balanced output), than the max pre-gain usable before clipping will be +6dbu (15+6=21), so in that sense, yes, pre-gain is also used to eventually match the levels between source and amp (preamp), but it's hard to find such sources with so high default output levels